The Physics of Crystallization in a Dense Coulomb Plasma

from Globular Cluster White Dwarf Stars

Don WingetDepartment of Astronomy and McDonald Observatory

University of Texasand

Department of Physcis UFRGS Brasil

S.O. Kepler, Pierre Bergeron, Mike Montgomery, Fabi Campos, Leo Girardi, Kurtis Williams

OUTLINE

I. Historical & Astrophysical Context Quantum mechanics, cosmochronology and the equation of state (EoS) of matter

II. What We Can Learn From the DiskObstacles remain, even after 20 years

III. White Dwarf Physics from Globular Clusters Overcoming obstacles with globular clusters

OUTLINE

I. Historical & Astrophysical Context Quantum mechanics, cosmochronology and the equation of state (EoS) of matter

II. What We Can Learn From the DiskObstacles remain, even after 20 years

III. White Dwarf Physics from Globular Clusters Overcoming obstacles with globular clusters

White Dwarf Stars: Eddington’s “Impossible” Star

Sirius B

•1844: Bessel notices “wobble” in Sirius’ position

•1862: Alvan Clark directly observes a faint companion

White Dwarf Stars: Eddington’s “Impossible” Star

•Dark companion is hot and compact, roughly the size of Earth and the mass of the Sun•Interior, even if made of the smallest atoms, must be ionized•“ … to cool the star must expand and do work against gravity …” Eddington.•Heisenberg uncertainty principle and Pauli exclustion principle to the rescue – Fowler 1926

•Chandrasekhar (1931) limit •Mestel (1952) Theory: develops understanding of decoupled mechanical and thermal properties:

ions electrons

White Dwarf Flavors

•Endpoint of evolution for most stars•Homogeneous

–Narrow mass distribution–Chemically pure layers

•Uncomplicated–Structure–Composition–Evolution dominated by cooling: (oldest=coldest)

They Shed Their Complexity!

White Dwarf Stars:

… and why are they interesting?

• Representative (and personal)– 98% of all stars, including our sun, will become one– Archeological history of star formation in our galaxy

=> White Dwarf Cosmochronology

• A way to find Solar Systems dynamically like ours

• Exploration of Extreme physics– Matter at extreme densities and temperatures

• 60% of the mass of the Sun compressed into star the size of the Earth

– Chance to study important and exotic physical processes: plasmon neutrinos, search for dark matter in the form of axions , and study the physics of crystallization …

Observations of Coolest WDs

•Observations: finding the coolest white dwarf stars in a population

–Thin disk

–Open clusters

–Thick disk

–Halo

–Globular clusters

White Dwarf Cosmoshronology

Calculate the ages of the coolest white dwarf stars:

White dwarf cosmochronology• Critical theoretical uncertainties for

dating the coolest WDs– Outer layers

• Convection, degeneracy, and radiative opacity control throttle

– Interiors• Neutrino emission in the hot stars

• Crystallization and phase separation in coolest

• Compare with observed distribution, and repeat the cycle…

(log P, log T) plane

Hot pre-white dwarfmodel

cool white dwarfmodel

Various physical processes thought to occur in WDs as they cool

The DB“Gap”

OUTLINE

I. Historical & Astrophysical Context Quantum mechanics, cosmochronology and the equation of state (EoS) of matter

II. What We Can Learn From the DiskObstacles remain, even after 20 years

III. White Dwarf Physics from Globular Clusters Overcoming obstacles with globular clusters

The Disk Luminosity Function

Fontaine, Brassard, & Bergeron (2001)

DeGennaro et al. (2008) Disk LF 3358 new SDSS WDs (with spectra)

shows the lower left portion of the reduced proper motion diagram from SDSS Data

Release 2.

Going after the cool WDs: Mukremin Kilic ….

HET Spectra of Cool White Dwarf Stars

The Disk vs M4: Globular clusters are older than the disk ….

Hansen & Liebert (2003)

OUTLINE

I. Historical & Astrophysical Context Quantum mechanics, cosmochronology and the equation of state (EoS) of matter

II. What We Can Learn From the DiskObstacles remain, even after 20 years

III. White Dwarf Physics from Globular Clusters Overcoming obstacles with globular clusters

White Dwarf Stars in Clusters

• Explore white dwarf cooling ages as compared to main sequence isochrone ages

• Open clusters help in establishing constraints on disk age

• Older open clusters sample critical physics of white dwarf cooling

• Minimize problems with birthrates

• Globular Clusters: Finally, we can isolate masses and explore the physics!

NGC 6397

NGC 6397 with HST AC

ComparingTheoretical

models:new(er)

opacities, interior EOS and

atmospheric boundary conditions

Hansen & Liebert (2003)

Fontaine 2001 models and Winget et al. 2008 models 0.5 Msun

Conclusions from model comparisons• Mass – radius is consistent for all groups

– EoS improvements ( Chabrier et al. 2000 over Lamb & Van Horn 1975 for interiors and Saumon Chabrier & Van Horn 1993 over Fontaine , Graboske & Van Horn 1977 for the envelope) do not produce (presently) observable differences in the models.

– Improved atmospheric surface boundary condition is not as important as has been claimed in the literature … it produces no observable differences until bolometric luminosities below the largest magnitude globular cluster stars

HST ObservationsHansen et al.

2007point sources

only

Data: proper motion screened sample from Richer et al. 2008, AJ, 135,2131

Fixing the WD evolutionary tracks in the

CMD by simultaneously

fitting the main sequence

and the WDsgives Z, (m-M)

and E

What advantages do we have over the disk population?

• The cooling sequences are “pinned” to the CMD by the main sequence and white dwarfs fitted together – sliding is not allowed.

• If we ignore the observational errors, the CMD location of a star uniquely determines its mass and radius: setting the mechanical properties of the white dwarf determined independently of the thermal.

• The mass range is very narrow.

• Ages provide some independent information … The terminus white dwarfs aren’t as old as you think!

Oops … the CIA hook is in the wrong place!

Luminosity Function for NGC 6397 proper motion screened WD sample

Richer et al. 2008 (proper motion)

Hansen et. Al. 2007

Richer et al. 2008 completeness

What physics might be relevant near the peak of theLuminosity Function

(the “clump” in the CMD)?

• Convective Coupling: The surface convection zone reaches the degeneracy boundary, reducing the insulation of the envelope

• Crystallization: Ions crystallize with attendant latent heat and phase separation expected from theory

Fontaine, Brassard & Bergeron (2001)

Crystallization Visuallization a cartoon by M.H. Montgomery

Ratio of Coulomb Energy to Ion Thermal Energy

What is the expected value of Gamma at crystallization?

(OCP) = 176 (Potekhin & Chabrier 2000, DeWitt et al. 2001, Horowitz, Berry & Brown 2007)

(MIX)= 230 - 260 (Horowitz, Berry & Brown 2007)

This is at the frontier of (brute force) molecular dynamics

Ratio of Coulomb Energy to Ion Thermal Energy

What is the value of Gamma at and near the “clump” in the observed CMD, or equivalently, the value of Gamma at and before (rise) the peak of the Luminosity Function?

log rho = 6.32 log T = 6.40 … nearly independent of composition!

(peak) = 194 (carbon) = 313 (oxygen)

(rise) = 182 (carbon) = 291 (oxygen)

Richer et al. 2008 completeness

Conclusions from NGC 6397• Confirm that crystallization occurs• Confirm that Debye cooling occurs• We can measure the Gamma of crystallization• Low metallicity clusters may not produce significant

O in cores of some of the 0.5Msun stars … or Brown and collaborators are right and Gamma = 230 - 260

• We find the first empirical evidence that Van Horn’s 1968 prediction is correct: Crystallization is a first order phase transition

The End

Thank you